BANGKOK, May 16 (Reuters) - Thailand's Senate said on Friday it was ready to choose an interim prime minister to end a political deadlock but stopped short of throwing out a beleaguered caretaker government and risking a violent backlash by its supporters.

The caretaker administration loyal to Yingluck Shinawatra, who was ousted as prime minister by a court last week, wants to organise a fresh election it would likely win.

But anti-government protesters backed by the royalist establishment want to see a new "neutral" interim premier to oversee electoral changes to end the influence of Yingluck's brother, ousted former premier Thaksin Shinawatra.

The Senate is the only legislative assembly still functioning after six months of anti-government protests and a disrupted February election that was later declared void.

A Senate working group has been consulting public and private sector representatives on a way out of the impasse and presented its suggestions on Friday.

"The Senate wants to solve the country's problems by having a prime minister with full powers," newly elected Senate Speaker Surachai Liengboonlertchai told reporters.

"If necessary, the Senate is prepared to open a special session to bring in a prime minister," he added.

But Surachai stopped short of calling on the caretaker government to step down. He said the people the Senate team consulted agreed that if the crisis dragged on "the economy and national security will be affected". The working group would meet the government on Monday, he said.

Anti-government protest leader Suthep Thaugsuban, a former deputy prime minister in a government run by the pro-establishment Democrat Party, expressed frustration with the Senate's failure to force the government out.

"The Senate's lack of an answer shows how our political system is unable to do anything," he told reporters outside parliament where thousands of his supporters are camped out.

Thousands of the government's "red shirt" supporters are rallying on the outskirts of Bangkok, clinging to hopes for an election that would return Thaksin's loyalists to power. They have warned of violence if the government is ousted.

"FULL FORCE"

The turmoil that began with anti-government protests in November is the latest phase in nearly a decade of animosity between the Bangkok-based establishment and Thaksin, a former telecommunications billionaire who won huge support among the rural and urban poor.

He was dogged by accusations of corruption, heavy-handed rule and even disrespect towards the monarchy and was deposed by the military in a 2006 coup. He has lived in self-exile since 2008 but exerts huge influence from abroad.

The anti-government protesters accuse Thaksin of using his vast wealth to woo poor voters, ensuring victory for his party in every election since 2001.

But critics say it would be unconstitutional for the Senate to appoint an interim prime minister, and the caretaker government says it still has a mandate to organise a new election and let the people decide.

It had tentatively set a July 20 date for an election, but the Election Commission says it needs more time.

Acting Prime Minister Niwatthamrong Boonsongphaisan, appointed after Yingluck's ouster, was forced to flee from a meeting with election officials on Thursday when protesters broke into the compound where talks were being held.

That came hours after a gun and grenade attack on anti-government protests in Bangkok's historic area in which three people were killed, the deadliest violence since February.

The attack prompted the army chief to warn that his men "may need to come out in full force" if violence escalates. Twenty-eight people have been killed since November.

Suthep has threatened to set up a "people's assembly" if the Senate does not install an interim premier and has called a meeting for Saturday at Government House, the prime minister's official offices, which have been abandoned for weeks. (Additional reporting by Aukkarapon Niyomyat; Editing by Robert Birsel)

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